Abstract. We give a complete list of all homogeneous spaces M = G/H where G is a simple compact Lie group, H a connected, closed subgroup, and G/H is simply connected, for which the isotropy representation of H on TpM decomposes into exactly two irreducible summands. For each homogeneous space, we determine whether it admits a G-invariant Einstein metric. When there is an intermediate subgroup H < K < G, we classify all the G-invariant Einstein metrics. This is an extension of the classification of isotropy irreducible spaces, given independently by O. V. Manturov [Ma1, Ma2, Ma3] and J. Wolf [Wo1,Wo2].
Abstract. We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with rank(M ) > 1, not isometric to a compact Lie group. Whenever there exists a closed proper subgroup G of Isom(M ) acting transitively on M we find all G-homogeneous (non-symmetric) Einstein metrics on M .
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